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KAM theory, Lindstedt series and the stability of the upside-down pendulum

Bartuccelli, M. V., Gentile, G. and Georgiou, K. (2003) KAM theory, Lindstedt series and the stability of the upside-down pendulum Discrete and Continuous Dynamical Systems, 9. pp. 413-426.


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We consider the planar pendulum with support point oscillating in the vertical direction; the upside-down position of the pendulum corresponds to an equilibrium point for the projection of the motion on the pendulum phase space. By using the Lindstedt series method recently developed in literature starting from the pioneering work by Eliasson, we show that such an equilibrium point is stable for a full measure subset of the stability region of the linearized system inside the two-dimensional space of parameters, by proving the persistence of invariant KAM tori for the two-dimensional Hamiltonian system describing the model.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Bartuccelli, M.
Gentile, G.
Georgiou, K.
Date : 1 March 2003
Uncontrolled Keywords : KAM theory, Lindstedt series, nonlinear Mathieu’s equation, vertically driven pendulum, upside-down pendulum, averaging, perturbation theory, stability.
Additional Information : First published in Discrete and Continuous Dynamical Systems, 9, 413-426. © 2003 American Institute of Mathematical Sciences.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:40
Last Modified : 16 Jan 2019 16:21

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